Starting only two Champions League games this season Sturridge was an unused sub in the final, but at 29 will have no shortage of suitors after previous spells at Man City and Chelsea.
Liverpool also said defender Alberto Moreno would depart Anfield at the end of his current deal.
Liverpool manager Jurgen Klopp told the club’s website: “The most important words to say to these two remarkable players is, ‘Thank you’.”
Sturridge joined Liverpool from Chelsea in January 2013 and went on to score 67 goals in 160 appearances for them.
“Daniel has earned the right to be considered a modern-day Liverpool great,” Klopp said. “Some of the goals he has scored for Liverpool were so, so, so important.”
Moreno arrived at Anfield from Sevilla in August 2014, playing 141 games for the club.
“They were here when I arrived as manager and during that period they — as much as anyone — helped to establish us as a team that would be heading in the right direction,” Klopp added.
“Without them we wouldn’t be the team and club we are in this moment.”